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Focusing of spherical nonlinear pulses in \(\mathbb{R}^{1+3}\) and absorption. (Absorption d’impulsions non linéaires radiales focalisantes dans \(\mathbb{R}^{1+3}\).) (French. Abridged English version) Zbl 0988.35120

Summary: We study the validity of geometric optics for nonlinear wave equations in three space dimensions whose solutions, pulse like, focus at a point. If the amplitude of the initial data is sufficiently big, strong nonlinear effects occur. When the equation is dissipative, pulses are absorbed. When the equation is accretive, the family of pulses becomes unbounded.

MSC:

35L70 Second-order nonlinear hyperbolic equations
78A05 Geometric optics
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